There is often a need to cut portions from a web of material, such as paper, for example for producing labels, adhesive stickers, tickets and the like, which web of material may have printing thereon, and may comprise two layers secured together by adhesive. The individual cut-out portions, which correspond for example to images of patterns printed on the web, may be punched or cut out of the web of material by cylindrical cutting or punching blades which rotate continuously, the web also moving uniformly in its longitudinal direction and passing over support or backing rollers to support the pressure of the blades on the web. The advantage of such cylindrical blades is that they have a high output capacity. However, they are relatively expensive to produce so that frequently they cannot be used for producing short runs of products, for cost reasons. Alternatively, the portions may be cut out by flat punching or cutting blades which can be relatively simple and therefore cheap to produce. However, these blades generally suffer from a low output capacity. Added to this is the fact that it is not possible for the individual cut-out portions to be stamped or punched out without a spacing between them, when the web passes continuously through the blades.